Lightroom requires me to sign in 3 or 4 times whenever I use it.
I get confronted with a screen telling my trial has 00 days left and I must license or sign in to continue.
If I simply ignore any of these repeated requests, Lightroom immediately exits
.This happens whether or not I sign in to Creative Cloud before attempting to launch Lightroom.
My subscription is in good standing and Lightroom/ Photoshop are up to date. There are no earlier versions installed.
From what you report it appears that you have a trial version of Lightroom 5 perpetual license version installed. Subscribing to the Creative Cloud package PS CC and Lightroom will not activate this version. Try the following.
1. Uninstall Lightroom using the OS system normal uninstall process. This will not affect your existing Catalog and user files and but will just remove the Lightroom Application.
2. Reboot your computer.
3. Open the Adobe Creative Cloud Application Manager and it should give you the option to download the latest Lightroom 5 install package. Proceed to download and install this version and it should be activated automatically, no requirement to enter any license key like the Perpetual License version. It will automatically link to your existing Catalog files etc.